Game theory

5 articles

Nim Nash equilibrium Cooperative game Non cooperative game theory Sequential game Stochastic game Bargaining Market design Search and matching theory Max min inequality Drama theory Confrontation analysis Walrasian auction Game theory on networks Social choice theory Mathematical programming with equilibrium constraints Asynchrony Backward induction Battle of the sexes Bayes correlated equilibrium Bayesian efficiency Bayesian game Bayesian nash equilibrium Bayesian regret Behavioral strategy Berge equilibrium Bertrand competition Bertrandedgeworth model Bertrands ballot theorem Best response Blotto game Centipede game Chicken Common knowledge Complete information Complete mixing Conjectural variation Constant sum Contingent cooperator Coordination game Correlated equilibrium Countersignaling Cournot competition Cournot game Cursed equilibrium Deadlock Dictator game Diners dilemma El farol bar problem Electronic mail game Epsilon equilibrium Expected utility hypothesis Fair cake cutting Fair division Farsightedness Focal point Folk theorem Game of chicken Game theory in communication networks General equilibrium theory Glicksbergs theorem Grim trigger Guess 2 3 of the average Hierarchy of beliefs Imperfect information Incomplete information Individual rationality Induction puzzles Information set Iterated elimination of dominated strategies Keynesian beauty contest Kuhns theorem Ky fan inequality Markov perfect equilibrium Markov strategy Matching pennies Max dominated strategy Mean payoff game Mertens stable equilibrium Metagame analysis Minimax algorithm Minimax theorem Minimum effort game Mutual knowledge Mutual knowledge logic N player game Nash equilibria Nash equilibrium computation Non credible threat One shot deviation principle Optional prisoners dilemma Outcome Pareto efficiency Parthasarathys theorem Payoff dominance Peace war game Perfect bayesian equilibrium Perfect information Perfect recall Pirate game Platonia dilemma Ply Princess and monster game Prisoners dilemma Program equilibrium Proper equilibrium Public goods game Pure strategy Purification theorem Quantal response equilibrium Quasi perfect equilibrium Rationalizable strategy Rendezvous problem Risk dominance Rock paper scissors Satisfaction equilibrium Self confirming equilibrium Sequential equilibrium Signalling Simultaneous action selection Simultaneous game Social trap Solution concept Spite Stackelberg competition Stag hunt Stochastically stable equilibrium Strategic complements Strategic dominance Strategic fair division Strategic form Strategic move Strategy Strong nash equilibrium Subgame Subgame perfect equilibrium Succinct game Superrationality Swap regret Tit for tat Topological game Tragedy of the commons Travelers dilemma Trembling hand perfect equilibrium Truel Trust game Truthful cake cutting Two level game theory Ultimatum game Uncorrelated asymmetry Unscrupulous diners dilemma Utility function Volunteers dilemma Von neumannmorgenstern utility theorem Wait walk dilemma Winstay loseswitch Winwin game Zero sum Zero sum game Zero sum problem Albert w tucker Alvin e roth Amos tversky Anatol rapoport Antoine augustin cournot Appeasement Ariel rubinstein Behavioral game theory Bertrand edgeworth model Bounded rationality Collusion Competitive altruism Complete contract Computational complexity of games Conflict escalation Contract theory Coopetition Cultural group selection David k levine David m kreps De escalation Deterrence theory Donald b gillies Drew fudenberg Dynamic inconsistency Edgeworth price cycle Eric maskin Escalation of commitment Evolution and the theory of games Fishers principle George r price Gibbs lemma Gift exchange game Harold w kuhn Helly metric Herbert scarf Heresthetic Herv moulin Hobbesian trap Incomplete contracts Inequity aversion Jean fran ois mertens Jean tirole Jennifer tour chayes John conway John maynard smith John nash Ken binmore Kenneth arrow Leonid hurwicz Martin shubik Melvin dresher Merrill m flood Mobbing Move by nature Multi agent system Myerson satterthwaite theorem Negotiation theory Obligationes Olga bondareva Open loop model Oskar morgenstern Paul milgrom Peyton young Preference Prim read theory Quantum game theory Rational agent Rational ignorance Rational irrationality Rationality Reinhard selten Robert aumann Robert axelrod Robert b wilson Roger myerson Samuel bowles Social software Strategic interaction Suzanne scotchmer Terminal investment hypothesis Thomas schelling Vickrey clarke groves mechanism William donald hamilton William vickrey Win win game Affine minimal surface Automata minimization of Branching point Maximal and minimal extensions Maximal and minimal operators Maximization and minimization of functions Maxima and minima Maximum and minimum points Minimal discrepancy method Minimal functional calculus Minimal iteration method Minimal normal subgroup Minimal property Minimal propositional calculus Minimal sufficient statistic Minimax principle Minimax property Minimax statistical procedure Minimization methods for functions depending strongly on a few variables Minimization of an area Minimization of the labour of calculation Minimizing sequence Minimizing sequence for an operator Minimum Nash theorem Non cooperative game Saddle point in game theory Solution in game theory Stability in game theory Strong relative minimum Sullivan minimal model Unimodular element Unimodular transformation Weak relative minimum

Combinatorics & Discrete Math LicenceExplication10 min

The Announcement That Told Nobody Anything

A stranger says out loud what every islander can already see, and ten days later ten people leave. The fact was mutual knowledge all along; what the announcement supplied was the nine levels of nested knowledge above it. An explicit count over 4096 possible worlds settles the induction without trusting it.

Probability & Statistics LicenceExplication10 min

Three Rolls, One Decision, and 14/3

A die is rolled up to three times and you are paid the face you stop on. The reflex answer of 3.5 is the value of the same game with the right to stop deleted, and the real value is 14/3, reached by computing the game from its last roll backwards. The thresholds move as rolls run out, which is why a four is worth keeping late and worth rejecting early.

Foundations & Logic LycéeExplication11 min

Blue, and the Two Sentences That Contain No Answer

Of the eight colour triples, seven are feasible from a pool of three blue hats and two red. The first silence removes one, the second removes two more, and all four survivors put a blue hat on the third man, which is what makes his answer a deduction rather than a lucky call. A pool sweep shows three blue and two red is the only small pool where the story can happen.

Combinatorics & Discrete Math LycéeExplication9 min

Say Six: The Only Opening That Wins the Race to Fifty

Counting to fifty in steps of one to ten, the first player wins, and exactly one of the ten legal openings does it. The stations are 6, 17, 28, 39 and 50, spaced eleven apart because eleven is one more than the largest legal step. The article carries the residue argument that proves the opening is unique, and the target 55 where the advantage flips.

Combinatorics & Discrete Math LicenceAnalyse9 min

The Weakest Player Should Waste the Turn

You hit one time in ten, your two opponents three and six, and you shoot first. Firing into the air is worth 965/4736 = 20.376%, which beats removing the strongest player by 0.195 percentage points, because a landed hit drops you into the duel you must enter second at 7/37 rather than first at 10/37. The article carries all three option values, the fixed points they solve, and the single Nash equilibrium that turns the usual assumption into a conclusion.